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Signal Processing and Sampling Method for Obtaining Time Series Corresponding to Higher Order Derivatives

机译:用于获取与高阶导数相对应的时间序列的信号处理和采样方法

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摘要

For modeling and controlling dynamic phenomena it is important to establish with higheraccuracy some significant quantities corresponding to the dynamic system. For fast phenomena, such significant quantities are represented by the derivatives of the received signals. In case of advanced computer modeling, the received signal should be filtered and converted into a time series corresponding to the estimated values for the dynamic system through a sampling procedure. This paper will show that present-day methods for computing in a robust manner the first derivative of a received signal (using an oscillating system working on a limited time interval and a supplementary differentiation method) can be extended to the robust computation of higher order derivatives of the received signal by using a specific set of second-order oscillating systems (working also on limited time intervals) so as estimative values for higher-order derivatives are to be directly generated (avoiding the necessity of additional differentiation or amplifying procedures, which represent a source of supplementary errors in present-day methods).
机译:为了建模和控制动态现象,重要的是建立更高的理想与动态系统相对应的一些重要数量。对于快速现象,这种显着的数量由接收信号的衍生物表示。在高级计算机建模的情况下,应通过采样过程将接收信号滤波并转换为对应于动态系统的估计值的时间序列。本文将显示,以稳健方式计算的本日方法,所接收信号的第一导数(使用在有限时间间隔和补充差分方法上工作的振荡系统)可以扩展到更高阶导数的鲁棒计算通过使用特定的二阶振荡系统(在有限的时间间隔上工作)来接收信号,以便直接产生高阶导数的估计值(避免所需的附加分化或放大程序的必要性本日方法中的补充误差的源。

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